Everton have appealed against the red card shown to Darron Gibson for this challenge at West Ham. Photograph: Tony O'Brien/Action Images

Everton will have Darron Gibson available for their Boxing Day game against Wigan Athletic having lodged an appeal with the Football Association over his dismissal at West Ham United.

The Republic of Ireland international received a straight red card from the referee, Andrew Taylor, on Saturday for a high challenge on Mark Noble. West Ham's Carlton Cole had earlier seen red for a similar challenge on Leighton Baines.

Everton are already without Marouane Fellaini through suspension for their festive home matches against Wigan and Chelsea and can ill-afford to lose Gibson to a three-match ban. The midfielder will face Roberto Martínez's side as Everton submitted an appeal to the FA on Monday and the case will not be reviewed by its disciplinary panel until Thursday.

David Moyes, the Everton manager, said: "We think there are real reasons to ask the FA to look at it again. You get fed up beating the drum and I don't want to be someone who continually lambasts referees – it is a hard enough job as it is – but I think we've had a raw deal of it this season, I really do.

"No manager wants to be critical of referees but it seems we are talking about their decisions most weeks.

"The referee at West Ham made a very quick decision on both red cards when maybe he could have paused and thought about it more. But then I'm not the person who trains referees. They get that from their assessors."

Moyes was more aggrieved at the assistant referee's decision to disallow a goal from Leon Osman at West Ham and that the controversy detracted from Everton's first Premier League away win since September.

Ahead of the Wigan game the Everton manager preferred to pay tribute to Phil Neville, who is set to make the 500th Premier League appearance of his career.

The 35-year-old Neville will become only the seventh player to reach that milestone after Ryan Giggs, Sol Campbell, Gary Speed, David James, Frank Lampard and Emile Heskey.

"The achievement says a lot about Phil but it doesn't surprise me," said Moyes. "His mentality and his attitude has always been great. He has been a great signing for us from Manchester United. I've spoken to him about carrying on [next season] but there is no great panic to make a decision. He has just come back from a knee operation and wants to see how his body is before he decides."